
<p>Interval Notation / Absolute Value Worksheet Answers</p><p>Graph the given intervals and find their intersection.</p><p>1. ( -3, 2) and [ 1 , 4 ) intersection = [ 1 , 2 )</p><p>-3 1 2 4</p><p>2. ( - ∞, 3 ) and ( - 2 , + ∞ ) intersection = ( - 2 , 3 )</p><p>-2 3</p><p>Solve and graph each inequality.</p><p>3. 6x 2 5 7 6x 2 5 6 2 2 6x 7 Divided by a negative, inequality 6x 7 switches direction 6 6 7 x 6</p><p>7 4. 1 2x 3 4 x 1 , x 2 1 2x 3 4 3 3 3 2 2x 7 2 2x 7 1 7 2 2 2 2 7 1 x 2 1 5. x 1 x 0 2 TTTT FFFFFFFFF TTTT Critical points are … 1 1 1 x 1 0 and x 0 2 2 1 1 1 1 2 2 1 x 1 and x 2</p><p>TEST x = 0</p><p> 1 0 10 0 2 1 1 0 2 1 0 2</p><p>FALSE</p><p> 2 1 6. x x x 0 3 3 Critical points are … 2 1 x 0 and x 0 and x 0 3 3 2 1 x 0, x , x 3 3</p><p>TEST x = 1 TTTT FF TTT FFFF 2 1 11 1 0 1 2 3 3 0 3 3 1 4 1 0 3 3 4 0 FALSE 9 7. 4x3 6x 2 0 Critical points are … FFFF TTTT FFFF 2x 2 2x 3 0 0 3</p><p>2 2 2x 0 2x 3 0 3 x 0 x 2</p><p>TEST x = 1</p><p>413 612 0 4 6 0 TRUE 2 0</p><p>Solve the absolute value equations.</p><p>8. 6x 5 0</p><p>6x 5 0 5 5 6x 5 5 x 6</p><p>CHECK</p><p> 5 6 5 0 6 5 5 0 0 0 0 0 2 9. x 1 3 x 1 4 0 Let u = x 1</p><p> u 2 3u 4 0 u 4u 1 0</p><p> x 1 4 0 x 1 4</p><p>No solution, abs. value ≠ (-)</p><p> x 1 1 0 x 1 1</p><p>1 x 1 1 1 x 1 1 Solution set x = { 0 , - 2 } 1 1 1 - 2 x 0</p><p>CHECK</p><p>0 1 2 30 1 4 0 1 2 31 4 0 1 3 4 0 0 0</p><p> 2 1 2 3 2 1 4 0 1 2 31 4 0 1 3 4 0 0 0 Solve and find the solution for each absolute value inequality as an interval.</p><p>10. x 2 1</p><p>1 x 2 1 2 2 2 1 3 1 x 3 Interval ( 1 , 3 )</p><p>11. x 3 3</p><p> 3 x 3 3 - 6 0 3 3 3 6 x 0 Interval ( - ∞ , -6 ] U [ 0 , + ∞ )</p><p>12. 2x 1 1</p><p>1 2x 1 1 - 1 0 1 1 1 2 2x 0 Interval ( - ∞ , -1 ] U [ 0 , + ∞ ) 2 2x 0 2 2 2 1 x 0</p><p>1 2 13. 2x 3 3 1 1 2 6 2 1 2 2x 3 3 3 1 1 1 3 3 3 1 1 Interval , , 1 2 6 2x 1 3 1 1 x 6 2</p>
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